89.11.18 problem 18

Internal problem ID [24543]
Book : A short course in Differential Equations. Earl D. Rainville. Second edition. 1958. Macmillan Publisher, NY. CAT 58-5010
Section : Chapter 8. Linear Differential Equations with constant coefficients. Exercises at page 117
Problem number : 18
Date solved : Thursday, October 02, 2025 at 10:46:00 PM
CAS classification : [[_high_order, _missing_x]]

\begin{align*} y^{\prime \prime \prime \prime }-2 y^{\prime \prime \prime }-13 y^{\prime \prime }+38 y^{\prime }-24 y&=0 \end{align*}

✓ Maple. Time used: 0.002 (sec). Leaf size: 29

ode:=diff(diff(diff(diff(y(x),x),x),x),x)-2*diff(diff(diff(y(x),x),x),x)-13*diff(diff(y(x),x),x)+38*diff(y(x),x)-24*y(x) = 0; 
dsolve(ode,y(x), singsol=all);
 

\[ y = \left (c_1 \,{\mathrm e}^{7 x}+c_2 \,{\mathrm e}^{6 x}+c_4 \,{\mathrm e}^{5 x}+c_3 \right ) {\mathrm e}^{-4 x} \]

✓ Mathematica. Time used: 0.002 (sec). Leaf size: 36

ode=D[y[x],{x,4}] -2*D[y[x],{x,3}] -13*D[y[x],{x,2}] +38*D[y[x],x] -24*y[x] ==0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to c_1 e^{-4 x}+c_2 e^x+c_3 e^{2 x}+c_4 e^{3 x} \end{align*}

✓ Sympy. Time used: 0.111 (sec). Leaf size: 27

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(-24*y(x) + 38*Derivative(y(x), x) - 13*Derivative(y(x), (x, 2)) - 2*Derivative(y(x), (x, 3)) + Derivative(y(x), (x, 4)),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

\[ y{\left (x \right )} = C_{1} e^{- 4 x} + C_{2} e^{x} + C_{3} e^{2 x} + C_{4} e^{3 x} \]